The technique of scanning microwave impedance microscopy (MIM) characterizes the local complex conductivity of a material, shedding light on the spatial profile of electronic states. In recent years, MIM has shown great promise for the investigation of topological phases and correlated quantum matter. In this talk, I will discuss the development of a new 3D imaging approach that resolves quantum states on individual atomic planes of a van der Waals heterostructure at temperatures down to 50 milliKelvin. By visualizing charge density fluctuations on different atomic planes, we shed light on the impact of surface impurities and screening on the formation of fractional quantum Hall states. Finally, by combining microscopy with the toolbox of information theory, we present an approach that algorithmically quantifies the entropy of the system, which can be used to shed light on hidden order, quantum criticality, and the microscopic nature of phase transitions.